Varying Coefficient Tensor Regression

Li Jialiang

Abstract: We propose a new varying coefficient model for tensor data regression analysis. To manage the complexity of multi-dimensional tensors, we first employ a tensor partitioning strategy to reduce dimensionality, followed by a tensor decomposition technique for the tensor covariates. By extracting key features from the tensor covariates, we feed these low-dimensional representations into a varying coefficient model, alongside other one-way covariates. Additionally, we apply a non-concave penalty estimation to simultaneously identify the model structure and select significant predictors. A subsequent refined smoothing step enhances the model's accuracy. We study the asymptotic properties of estimated functions and coefficients. Extensive simulations are conducted to evaluate the performance of our approach. Our study is motivated by a real fundus image dataset, which is analyzed using our model to improve glaucoma management.

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Submission Type: Special issue on High-Dimensional Data Modeling

Submission Number: 3